Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120

Mavrodiev Strachimir Chterev,Vol Alexander

doi:10.11648/j.ns.20190402.11

Mavrodiev Strachimir Chterev, Vol Alexander

Open Access

https://doi.org/10.11648/j.ns.20190402.11

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Abstract

George Gamow’s liquid drop model of the nucleus can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. Its semi-numerical equation was first formulated in 1935 by Weizsäcker and in 1936 Bethe [1, 2], and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Their formula gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons. Mavrodiev and Deliyergiyev [3] formalized the nuclear mass problem in the inverse problem framework. This approach allowed them to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. They formulated the inverse problem for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker going step-by-step through the AME2012 [4] nuclear database. The resulting parameterization described the measured nuclear masses of 2564 isotopes with a maximal deviation of less than 2.6 MeV, starting from the number of protons and number of neutrons equal to 1. The unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified procedure realized in the algorithms developed by Aleksandrov [5-7] to solve nonlinear systems of equations via the Gauss-Newton method. In the presented herein article we describe a further development of the obtained by [3] formula by including additional factors,- magic numbers of protons, neutrons and electrons. This inclusion is based the well-known experimental data on the chemically induced polarization of nuclei and the effect of such this polarization on the rate of isotope decay. It allowed taking into account resonant interaction of the spins of nuclei and electron shells. As a result the maximal deviation from the measured nuclear masses of less than 1.9 MeV was reached. This improvement allowed prediction of the nuclear characteristics of the artificial elements 119 and 120.

Highlights

In the last few years there has appeared new experimental data which demonstrated the dramatic change of decay rate due to the ionization of an atom and due to the resonant interaction between the electron shells and the nuclei [8,9,10,11,12,13,14].For example, a strong dependence of the nuclear decay rate on ionization was shown for the 229 Th 90, 226 Rn 88, 152 Eu 63, 154 Eu 63 isotopes and the 178 mHf 72, 99 mTc 43 isomers
Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120 interaction of nuclei and the electron shell for accuracy of a well-known formula expands our understanding of the structure of atoms and the possible contribution of nucleus interaction to the formation of compounds and biological structures
Following are the steps involved in the generalization of the BW mass formula

Summary

Introduction

In the last few years there has appeared new experimental data which demonstrated the dramatic change of decay rate due to the ionization of an atom and due to the resonant interaction between the electron shells and the nuclei [8,9,10,11,12,13,14]. Testing the effectiveness of accounting for the Mavrodiev Strachimir Chterev and Vol Alexander: Improved Numerical Generalization of the Bethe-Weizsäcker Mass. Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120 interaction of nuclei and the electron shell for accuracy of a well-known formula expands our understanding of the structure of atoms and the possible contribution of nucleus interaction to the formation of compounds and biological structures. Following are the steps involved in the generalization of the BW mass formula

Bethe-Weizsäcker Mass Formula Digital Generalization

About the Choice of Arguments for Solving the Inverse Problem

The Explicit Form of Unknown Functions

Description of Data

Discussion

Conclusion